Aspheric Holographic Optical Elements (HOEs) have been applied in areas such as optical testing, optical processing, and imaging. The aspheric HOE is generally represented during the design process in terms of its object and reference construction wavefronts, which may be defined in a number of ways such as point source locations, wavefront-forming lens surfaces, or analytic phase functions. We have pursued a design and fabrication process which takes advantage of the design flexibility provided by arbitrary analytic wavefront definitions. The goal of this process is to produce large, efficient, generally aspheric HOEs without the long lead times and high costs associated with fabricating generally aspheric wavefront-forming lenses. The physical realization of the HOE wavefronts is accomplished through a combination of readily-available lenses and computer-generated holograms (CGHs). An optical processor is employed in the wavefront-generating hardware which serves both to filter out unwanted CGH diffracted orders and to copy the filtered wavefront into a high-efficiency dichromated gelatin hologram. The processes of HOE wavefront definition, optical processor design, and CGH fringe generation are described along with practical limitations of the concept.